Volume 54, Issue 6, Pages 973-985 (June 2007) Purkinje Cells in Posterior Cerebellar Vermis Encode Motion in an Inertial Reference Frame  Tatyana A. Yakusheva, Aasef G. Shaikh, Andrea M. Green, Pablo M. Blazquez, J. David Dickman, Dora E. Angelaki  Neuron  Volume 54, Issue 6, Pages 973-985 (June 2007) DOI: 10.1016/j.neuron.2007.06.003 Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 1 Schematics Illustrating the “Reference Frame” and “Linear Acceleration” Problems, along with the Proposed Mathematical Solution (A) The “Reference frame” problem is illustrated by an example of two yaw rotations that are identical in head coordinates but differ in earth-centered coordinates. Yaw rotations in upright and supine orientations differ relative to the direction of gravity (gs, defining here the earth reference frame), yet elicit identical semicircular canal afferent responses that encode rotation, ω, in head-centered coordinates. (B) The “Linear acceleration” problem is described by schematizing that hair cells and otolith afferents encode net linear acceleration, α, thus respond identically to either translational, t, or gravitational, g, components. (C) Proposed computational solution, schematized as two steps (for details about the underlying mathematics, see Supplemental Data). To solve the “Reference frame” problem, neural estimates of g must be used by the brain to decompose the head-fixed canal activation, ω, into earth-vertical (ωEV, parallel to gravity) and earth-horizontal (ωEH, perpendicular to gravity) components. To solve the “Linear acceleration” problem, a change in angular orientation can be computed by temporal integration of ωEH. This signal (∫ωEH) can then be combined with net linear acceleration from otolith afferents to extract translation. Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 2 Typical Example of NU Purkinje Cell Responses (A–D) Instantaneous firing rate of a typical Purkinje cell during Translation (A), Tilt (B), Tilt − Translation (C), and Tilt + Translation (D) (0.5 Hz). Data are shown along four stimulation axes (cartoon drawings), with the translation/tilt position (bottom traces) being matched in both amplitude and direction to elicit an identical net acceleration in the horizontal plane. Straight black and curved gray arrows denote translation and tilt axes of stimulation, respectively. Vertical dotted lines mark the peak stimulus amplitude. (E and F) Summary of peak firing rate modulation amplitude (E) and phase (F) as a function of stimulus orientation, θ. Data are shown separately for Translation (filled squares, solid lines), Tilt (open squares, dashed lines), Tilt − Translation (filled triangles, solid lines), and Tilt + Translation (open triangles, dashed lines). Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 3 Summary of Purkinje Cell Responses Summary of neural responses during Tilt (A), Tilt − Translation (B), and Tilt + Translation (C), plotted as a function of the corresponding response during Translation (0.5 Hz) (n = 72). Dashed gray and solid black lines illustrate the predictions for “afferent-like” and “translation-coding” neurons, respectively. Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 4 Data after Canal Plugging (A–D) Instantaneous firing rate of a typical Purkinje cell during Translation, Tilt, Tilt − Translation, and Tilt + Translation (0.5 Hz). Same format as in Figures 2A–2D. (E and F) Summary of neural responses during Tilt and Tilt − Translation plotted as a function of the corresponding response during Translation (n = 19). Dashed gray and solid black lines illustrate the predictions for “afferent-like” and “translation-coding” neurons, respectively. Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 5 Scatter Plots of z Scores Corresponding to the Partial Correlation Coefficients for Fits of Each Cell Response with the “Translation-Coding” and “Afferent-like” Models (A) Data from n = 72 cells in labyrinthine-intact (black circles) and n = 19 cells in canal-plugged animals (gray circles) during 0.5 Hz motion stimuli. (B) NU Purkinje cell data (solid circles) are compared with those previously recorded in VN/FN neurons (open triangles). The superimposed dashed lines divide the plots into three regions: an upper left area corresponding to cell responses that were significantly better fit (p < 0.01) by the translation-coding model, a lower right area that includes neurons that were significantly better fit by the afferent-like model, and an in-between area that would include cells that were not significantly better fit by either model. Data shown for the cell's best-responding translation direction. Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 6 Canal-Driven Responses of Purkinje Cells Encode Rotation in an Earth-Centered Reference Frame (A–C) Instantaneous firing rate of the Purkinje cell of Figure 2 during earth-vertical axis rotation (coding of ωEV) with the monkey either upright ([A], Yaw rotation) or statically tilted ±45°, bringing the plane of rotation half-way between yaw and roll (B) or pitch (C) (see cartoon drawings). (D) Peak response modulation during earth-vertical axis rotation with the animal tilted ±30° and/or ±45° (as in [B] and [C]) plotted as a function of the corresponding prediction under the assumption that Purkinje cells encode rotation in a head-centered reference frame. If cerebellar neurons encode rotation in head coordinates, data should fall along the unity slope, dashed line (“head coordinates”). Alternatively, if they selectively modulate only during earth-horizontal (but not earth-vertical) axis rotation, data should fall along the abscissa (“earth coordinates”). Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 7 Evidence for Temporal Integration of Canal-Driven Signals Purkinje cell gain (A and B) and phase (C) during the Tilt − Translation stimulus condition (i.e., isolating the canal-driven response component) plotted as a function of frequency. Gain (in spikes/s per degree/s) and phase (in degrees) in (A) and (C) are expressed relative to the head velocity stimulus. Thin lines and symbols illustrate data from single neurons tested at different frequencies (n = 23; shown only for best-responding stimulus direction); thick lines indicate population averages. (B) shows the mean (±SD) of velocity and position gains (solid black and dashed gray lines, respectively). Velocity gains are expressed in units of spikes/s per degree/s. Position gains are expressed in spikes/s per degree. Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions

Figure 8 Spatiotemporal Matching of Canal-Driven and Otolith-Driven Signals (A) Response phase during the 0.5 Hz Tilt − Translation stimulus (canal-driven component) is plotted as a function of the respective phase during Translation (otolith-driven component) (n = 72; data along the best-responding stimulus direction). Phase has been expressed relative to tilt velocity. (B) Distribution of the difference in preferred directions between the 0.5 Hz Tilt − Translation and Translation stimulus conditions. Data (n = 16) from cells tested at multiple orientations (e.g., Figure 2) and fitted with a spatiotemporal model to compute preferred directions (Angelaki and Dickman, 2000). Neuron 2007 54, 973-985DOI: (10.1016/j.neuron.2007.06.003) Copyright © 2007 Elsevier Inc. Terms and Conditions